A Coevolution Algorithm Based on Spatial Division and Hybrid Matching Strategy

The Framework of MaOEA-SDAC

Algorithm 1 in Table 1 is the overall pseudo code of Many-Objective Optimization Algorithm based on Space-Partition and Angle-based culling strategy (MaOEA-SDAC). In Table 1, represents a vector of reference points, represents an initial population, represents an iterator, P_t represents the current generation t of a population, Q_t represents its offspring population generated by the recombination operation, R_t represents a population generated after the merger of P_t and Q_t, represents the next generation produced by P_t environmental selection.

In Table 1, lines 01-03 in algorithm MaOEA-SDAC initialize some operations for a population. Lines 05-21 are an iterative process of the population, which is also its core part. Lines 08-20 run some actions in its environmental selection stage of the population.

The specific process of MaOEA-SDAC is as follows. The first step generates reference points , initialize the population and set the number of iterations t=0. The second step enters a loop, and the condition of the loop judgment is whether the maximum number of iterations is reached. If the related condition is met, the solution set is output; otherwise, the loop is entered. In the cycle, is first matched and is selected to generate , then is cross-mutated to generate , and is generated by combining and . Do non-dominated sorting on , and merge the sorted result with to generate new . Then, a judgement condition will be entered, which is to generate the next population through environmental selection operation on . Lines 12 and 18 are two the strategies of spatial partitioning and angle-based Culling introduced by this algorithm MaOEA-SDAC.